I use the circle of 5ths (or used) to remember what accidentals are in the Major keys.
Start with C Major: CDEFGAB (no sharps)
Count up to the 5th note (G).
Count up to the 4th note (F)
Sharpen the 4th note (F becomes F#)
Write the scale out again, starting from G, with the new F#
GABCDEF# You've now constructed a G Major scale, YAY!
Continue along, so count up to the 5th note of G (D), count up the 4th note (C) sharpen the 4th note (C to C#) carry over the previous accidental from G Major (F#) so now you know the notes in D Major are:
DEF#GABC#.
Continue

For Major scales with flats, instead of counting up to the 5th note for the next scale, count up to the 4th (So F), instead of counting up to the 4th for the next accidental, count up to the 7th, then flatten it (B becomes Bb)
So we have F Major: FGABbCDE, which is the first Major scale with 1 flat, carry on up the process and you'll eventually get all of the major scales with all the flats, if you write all of these out you'll eventually know what accidentals/notes comprise all major scales in all keys.
If you do this enough you'll eventually just know them off by heart.
The circle of 5ths has also been used as a general modulation in many pieces, especially from the classical period. The guitar solo in Deep Purple's 'Burn' goes through a cycle of 5ths.
Too much typing, hands hurt!